Systems for increasing the sensitivity of gamma-ray imagers

ABSTRACT

Systems that increase the position resolution and granularity of double sided segmented semiconductor detectors are provided. These systems increase the imaging resolution capability of such detectors, either used as Compton cameras, or as position sensitive radiation detectors in imagers such as SPECT, PET, coded apertures, multi-pinhole imagers, or other spatial or temporal modulated imagers.

This application is a continuation of US. patent application Ser. No.11/607,554, titled “Methods for Increasing the Sensitivity of Gamma-RayImagers, ” filed Nov. 30, 2006, incorporated herein by reference, whichclaims priority to U.S. Provisional Patent Application Serial No.60/755,469, titled: “Methods for Increasing Sensitivity of Gamma-RavImagers” filed Dec. 29, 2005, incorporated herein by reference.

The United States Government has rights in this invention pursuant toContract No. DE-AC52-07NA27344 between the U.S. Department of Energy andLawrence Livermore National Security, LLC, for the operation of LawrenceLivermore National Laboratory.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to gamma ray imaging, and morespecifically, it relates to improving the gamma ray imaging efficiencyand accuracy of semiconductor detectors.

2. Description of Related Art

Most gamma-ray imaging systems use position sensitive scintillators. Ascintillator is a device or substance that absorbs high energy(ionizing) electromagnetic or charged particle radiation then, inresponse, fluoresces photons at a characteristic Stokes-shifted (longer)wavelength, releasing the previously absorbed energy. Such scintillatorshave good efficiency, but they lack good energy resolution, and theirposition resolution decreases significantly with increasing the energyof the radiation. Semiconductor detectors have the capability to providegood efficiency and position resolution, but also good energy resolutionand granularity. All these features are of interest for collimator basedimagers, but especially for Compton imagers. In fact the introduction ofposition sensitive semiconductor detectors helped revitalize the Comptonscatter camera concept in the last few years. Several Compton cameradevices based on CdZnTe, high purity Germanium and Silicon detectors areunder development targeting applications in astrophysics, bio-medicalresearch and homeland security. Some of these systems provide imageshaving good resolution, but most have very low efficiency. The reasonfor the low efficiency is that only a fraction of the total detectedphotons are found suitable for Compton imaging. To obtain reasonableresolution, the average distance between the interactions must be largeas compared with the position uncertainty of individual interactions, sothat only events with widely separated and clean interactions can beused for imaging. Improved efficiency must be demonstrated for a Comptonscatter camera to become a competitive gamma-ray imaging method.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide systems that improveimaging efficiency and accuracy of semiconductor detectors.

It is another object to provide systems that increase the number andaccuracy of events that can be imaged in Compton cameras.

Still another object of the invention is to increase the number andaccuracy of events that can be imaged in collimator based imagers.

Another object is to provide position interpolation systems fordetermining the position resolution in a segmented detector.

Another object is to provide systems that increase the granularity of adetection system by discriminating multiple interactions taking place inadjacent segments from single interactions that induce signals in twoadjacent segments.

These and other objects will be apparent based on the disclosure herein.

There are four main factors that affect the imaging efficiency ofCompton imagers: the detection quantum efficiency, the detectiongranularity, the position resolution and the energy resolution for eachinteraction. Improvement in detection quantum efficiency can be obtainedby optimizing the detection geometry and scaling up the imaging system.The methods of the present invention, however, mainly address positionresolution and detection granularity. In the case of most segmenteddetectors, the position resolution is determined by the detectiongranularity alone. As shown below, however, position resolution can beimproved by using position interpolation methods. Further, systemgranularity can be improved by discriminating multiple interactionstaking place in adjacent segments from single interactions that inducesignals in two adjacent segments. This will increase the reliability ofthe detected photons for Compton imaging as well as for other collimatorbased imagers.

The developed methods can be used to analyze data collected from doublesided segmented detectors (DSSDs) and pixilated semiconductor detectors,such as Si(Li), Ge and CdZnTe. The methods will increase the imageresolution and sensitivity of gamma-ray imaging systems used for DHS,DOE and DOD applications. Gamma-ray imagers are important insurveillance, monitoring, diagnostics and search applications.

A Compton camera using the invented methods will have potential use inmedical imaging and industry in a collimatorless imager. Apparatusesthat carry our such methods will enable semiconductor detectors ofincreased interest as high efficiency, high-resolution imagers inspatial or temporal modulated imagers. PET and SPECT imagers as well asother radiographic systems will be prime candidates.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate embodiments of the invention and,together with the description, serve to explain the principles of theinvention.

FIG. 1 is a chart showing the data flow between hardware components.

FIG. 2 shows an embodiment of the analysis methods.

FIG. 3 lists the methods that are part of the Signal Feature Extractiongroup.

FIG. 4 is a flowchart of the Comprehensive Event Selection method.

FIG. 5 is a graphical representation of the main parameters used inevent selection wherein E is Energy, T50 is 50% threshold timing and TSAis transient signal amplitude.

FIG. 6 shows the calibration of depth interpolation with a planar Gedetector.

FIG. 7 shows a 3D view of an experimental apparatus for measuringZ-depth.

FIG. 8A shows charge carriers produced in a interaction taking placeunder the border being collected by two adjacent segments.

FIG. 8B shows two adjacent segments collecting charge carriers from twoseparate interactions.

FIG. 9 shows the simulation of charge carrier drift and diffusion whereall electrons and holes were generated at the same point.

FIG. 10 is an example of signal waveforms produced by a charge sharinginteraction where the time interval represents the gap-test interval.

FIG. 11 shows signals induced in a charge sharing interaction takingplace away from the collecting electrode.

FIG. 12 shows signals induced in a charge sharing interaction takingplace close to the collecting electrode.

FIG. 13 is an experimental setup to study charge sharing interactions.

FIG. 14 is a histogram of gapTest values using gap test version 1.

FIG. 15 is a histogram of gapTest values using gap test version 2.

DETAILED DESCRIPTION OF THE INVENTION

Utilization of gamma-ray events with closely spaced interactionsrequires maximum detector granularity and position resolution. Despite asegment pitch size of at least 2 mm, position resolutions in thesub-millimeter range are obtained by using new waveform filteringmethods of the present invention. By analyzing the induced signals inadjacent segments of a segmented detector, the position of theinteraction within the segment width can be inferred. The depth ofinteraction is determined (within 0.5 mm in one embodiment) by measuringthe difference in the arrival time of the electrons and holes to theopposite electrodes. The best position resolution achievable with Gedetectors is ultimately limited by the path length of the electronsproduced in Compton or photoelectric interactions and the subsequentdiffusion of the charge carriers in the crystal. The reconstruction ofgamma-ray interactions implies the determination of the number ofinteractions in the active volume of the imager, as well as theirenergies and three-dimensional positions.

FIGS. 1-4 provide a general description of the invention. FIG. 1 showsthe data flow between hardware components of an exemplary embodiment. Atleast one double-sided segmented detector (DSSD) 10 is provided fordetection of gamma rays. The DSSD is connected to and in communicationwith data acquisition electronics 12, which at least containpreamplifiers for each channel, analog-to-digital converters and fastprocessing electronics (FPGA and/or digital signal processing (DSP)).The data acquisition electronics 12 are in communication with a computer14. The algorithms presented in this disclosure may be implemented inthe data acquisition electronics 12 and/or the computer 14.

FIG. 2 is a chart of the main analysis methods groups. Signal featureextraction methods 20 contain filters applied on the digitized signalsthat extract parameters required for the next analysis step, referred toas Comprehensive Event Selection 22. This group (22) of methods containsalgorithms used to determine energies and positions of gamma-rayinteractions. Gamma-ray interactions can be Compton scatterings,photoelectric absorptions or pair-productions. The Further Analysismethods 24 use the list of interactions to create gamma-ray images.

FIG. 3 shows a Signal Feature Extraction 20 group of methods. Signaltriggering filter 30 determines the channels that have collected chargecarriers, electrons or holes. The “triggered channels” are also called“firing channels.” Energy filter 32 determines the energy deposited ineach firing channel. Time filter 34 determines the approximate time atwhich the charge carriers arrive at the detector electrode for eachfiring segment. A T50 timing filter (discussed below) can be used.Transient signal amplitude filter 36 calculates the signal amplitudes inthe channels adjacent to the triggered ones. GapTest filter 38 is usedobtains data for later use in the GapTest if adjacent channels aretriggered.

FIG. 4 is a flowchart of Comprehensive Event Selection methods 22. Block40 shows energy matching of “1-1” firing segments, if any. Block 42shows the use of z-and x-y-interpolation algorithms to determine theposition of the interaction. Block 44 shows energy matching of “2-1”firing segments, if any are possible. Block 46 shows that if the twofiring segments on one side are adjacent, GapTest is performed. Block 48shows the use of z-and x-y-interpolation algorithms to determine theposition of the two interactions; if the GapTest was positive, use thez-and x-y-interpolation algorithms to determine the position of a singleinteraction. Block 50 shows the step of energy matching of “3-1” triggersegments, if any are possible. Block 52 shows that if the two firingsegments of Block 50 on one side are adjacent, GapTest is performed.Block 54 shows the use of z-and y-interpolation algorithms to determinethe position of the two interactions of Block 50; if the GapTest waspositive, use the z-and x-y-interpolation algorithms to determine theposition of a single interaction. Block 56 checks event integrity. Thisverifies that the sum of the energies of all identified interactions isconsistent with the total energy deposited in the detectors.

FIG. 5 is a graphical representation of the main parameters used inevent selection wherein E is Energy, T50 is 50% threshold timing and TSAis transient signal amplitude. FIG. 8A shows charge carriers produced inan interaction taking place under the border being collected by twoadjacent segments. FIG. 8B shows two adjacent segments collecting chargecarriers from two separate interactions. FIG. 9 shows the simulation ofcharge carrier drift and diffusion where all electrons and holes weregenerated at the same point. FIG. 11 shows signals induced in a chargesharing interaction taking place away from the collecting electrode.

A so-called Comprehensive Event Selection algorithm is used to match(compare) the information from firing segments in a Double-SidedSegmented Detector (DSSD). The result of this algorithm is a list ofinteractions taking place in the detector for each detected photon. Theparameters associated with each identified interaction are: energy, 3Dposition, detector identifier (in a system of multiple detectors), andconfidence level. For each event consisting of one or more interactions,the algorithm will deliver a figure-of-merit (FoM_CES) labeling theresult of the algorithm. A figure-of-merit between 0 and 1 will beattached to accepted events. Its value will be proportional with theconfidence level for the event as a whole. A figure-of-merit outside [0,1] will label an event which has firing segments that can not beproperly matched. In this case, the FoM_CES value will code the reasonfor the mismatch. Such an event is discarded for imaging purposes.

The algorithm uses as input a list of firing segment parameters. Theparameters associated to the firing segments are obtained in a previousstep in the data acquisition system (see FIGS. 3, 5 and 6). For eachfiring segment, the parameters provided are E, T50, R and gapTest, whereE [keV] is the deposited energy, T50 [ns] is the time when the pulsereaches 50% of its total amplitude, R is the ratio of the transientsignal amplitudes (TSA) of the two adjacent segments (described below),and gapTest is the parameter indicating the match in the waveform of thesignal from the present channel and the signal from a firing adjacentchannel, if present (described below).

As electron and hole recombination rates are negligible for Si(Li) andHPGe detectors, an equal number of electrons and holes are expected tobe collected on the opposite sides of a DSSD (the AC and DC sides). As aresult, the pulse amplitudes will be similar on both sides. Thisdiscussion arbitrarily assumes the use the AC segments to determine thex-coordinate of the interaction, and the DC segments to determine they-coordinate.

The segments are matched according to the proximity of the energybetween firing segments on opposite electrodes. The matching processcontains several successive steps. A first step of the algorithmattempts to match a single firing segment on one electrode with a singlefiring segment on the opposite electrode (1-1 matches). Afterwards, theremaining firing segments are checked as the sum of energies of any twofiring segments on one electrode against one firing segment on the otherelectrode (2-1 and 1-2 matches). 1-2, 2-1 and 2-2 matches are eithercaused by a single interaction or two interactions. A single interactionmay produce signals on two strips on the same side when the interactionoccurs in the gap between two strips. If the two firing segments on anelectrode are adjacent to each other, a model for a single interactiondepositing energy in the two segments (which we term as charge sharing)is checked upon. In the third step the higher multiplicity matches areanalyzed (the 2-2, 3-2, 2-3, 1-3, 3-1 matches).

For each assumed match, a matching likelihood P_(kl) is calculated toinclude probabilities for each segment firing to contain an interactionconsistent with the assumed model (P_(k) and P_(l)). A match is adoptedif the calculated likelihood is above a certain threshold. For 1-1matches, the match probability becomes:

$\begin{matrix}{{P_{kl} = {\frac{1}{\sigma\sqrt{2\;\pi}}{\mathbb{e}}^{\frac{- {({E_{k} - E_{l}})}^{2}}{\sigma^{2}}}P_{k}P_{l}}},} & (1)\end{matrix}$In this case, P_(k) and P_(l) represent the probability that the firingsegments have fired because of a single interaction, as opposed tomultiple interactions. E_(k) and E_(l) are the energies of the twosegments, and σ is the equivalent standard deviation of the measuredenergies.

For 1-2 or 2-1 matches, if the 2 firing segments on the same electrodeare non-adjacent, the assumed model accounts for 2 separate interactionsdepositing energy in a single segment on one side and in two segments onthe other side. The probability for the match becomes:

$\begin{matrix}{P_{{kl},{2\; l}} = {\frac{1}{\sigma\sqrt{2\pi}}{\mathbb{e}}^{\frac{- {({E_{k} - {\sum\limits_{{l\; 1},{l\; 2}}\; E_{{l\; 1},{l\; 2}}}})}^{2}}{\sigma^{2}}}P_{k,{2\; l}}{P_{{({{l\; 1},{l\; 2}})},{2\; l}}.}}} & (2)\end{matrix}$The term P_(k,2l) accounts for the probability of two interactionsinducing the signal in segment k. The term P_((l1,l2),2l) accounts forthe probability of one interaction in segment l1 and one interaction insegment l2.

If a single interaction is assumed to produce a charge-sharing instance,the probability is defined as:

$\begin{matrix}{P_{{kl},{CS}} = {\frac{1}{\sigma\sqrt{2\pi}}{\mathbb{e}}^{\frac{- {({E_{k} - {\sum\limits_{{l\; 1},{l\; 2}}\; E_{{l\; 1},{l\; 2}}}})}^{2}}{\sigma^{2}}}P_{k}{P_{{({{l\; 1},{l\; 2}})},{CS}}.}}} & (3)\end{matrix}$The term P_((l1,l2),CS) represents the probability for the signalwaveforms of two adjacent segments l1 and l2 to have been produced by asingle interaction in a charge sharing interaction. One alternative tothis model is a case of two separate interactions. Such a model ischecked upon by equation (2). Calculation of the probability termP_((l1,l2),CS) is described below under the description of the “gaptest”.

If no information exists to support the calculation of theP_((l1,l2),CS), P_((l1,l2),2l), P_(l) and P_(k) terms, the match is madeby simply taking the minimum value for the quadratic difference betweenthe segment energies:

$\begin{matrix}{\xi_{kl} = {\frac{\left( {E_{k} - E_{l}} \right)^{2}}{\sigma^{2}}.}} & (4)\end{matrix}$A match is accepted only if the overall likelihood is above a presetthreshold.Z Interpolation, Event Time Determination

An analysis of the signal waveforms is used to determine the position ofthe interaction within the detector thickness (z-interpolation). This ismade possible by measuring the time difference between the moments theelectrons and holes arrive at the electrodes. This time difference willrepresent the charge carriers relative drift time, which is proportionalto the depth of interaction.

Event Timing

The determination of the absolute event timing is important for thez-interpolation when the arriving time for one type of the carrierscannot be accurately measured. This is the case for the 2-1, 1-2, 3-1,1-3 matches. Whenever two or more signal components superpose in thetotal signal waveform, no reliable determination of the two arrivaltimes can be made using simple filters. However, if the absolute eventtime is known from a previous segment match, using only the arrival timefor the clean signal, the depth of interaction can be calculated.

The charge carrier arrival time is represented by the T50 timing. TheT50 timing is the time when the pulse reaches 50% of its totalamplitude. A digital filter designed to fit in the data acquisitionsystem provides the T50 timing. T50 is used as the time pick-off becausethe timing at 50% of the pulse amplitude in a segmented planar Gedetector is very close to the point of the steepest slope of the signalleading edge, where the best time resolution can be achieved. The T50timing is a good measure for the charge carrier collection time becausethe largest electric current induced in the electrodes is proportionalto the weighting fields, E_(w), of the collecting electrode,

$\begin{matrix}{{{I(t)} = {\sum\limits_{{{cc} = c},h}\;{{{qv}_{cc}(t)}{E_{w}\left( {r_{cc}(t)} \right)}}}},} & (5)\end{matrix}$where q is the electric charge of the carriers, v_(cc)(t) is their driftvelocity, r_(cc)(t) is their position, and cc stands for chargecarriers-electrons, e, and holes, h, and because of the small dimensionof the electrodes as compared with the detector thickness, the highestvalues for the weighting fields take place in the close proximity to theelectrode. Since the charge signal is an integral over the current

Q(t) = ∫_(−∞)^(t)I(t) 𝕕t,the largest variation takes place when the current is largest.Z-Interpolation

The arrival time for the electrons and holes is used to deduce therelative drift time, and through that, the depth of interaction. Sincethe electric fields inside the planar detector of about 1000V/cm areclose to the saturation in the drift velocity for both electrons andholes, in a first approximation, one can assume constant driftvelocities for the charge carriers in the range of electric fieldsexisting in the detector, so a linear function can approximated therelation between the depth of interaction, z, and the difference incollection times:z=z ₀ +k _(z) c(t _(e) −t _(h)),  (6)where t_(e) is the time when the electrons arrive at the electrode,t_(h) is the time when the holes arrive at the electrode, z₀ is aconstant which is close to the halfway point between the detectorelectrodes, the displacement which is due to the difference in thesaturated drift velocities between holes and electrons, and k_(z) is aproportionality factor. If no arrival time is known for one of thecarriers, but the absolute event time T_(o) is known, the following isused:z=v _(e)(t _(e) −T _(o)),  (7)orz=D−v _(h)(t _(h) −T _(o)),  (8)where D is the detector thickness, v_(e) is the effective saturationdrift velocity for electrons, and v_(h) is the effective saturationdrift velocity for holes. T_(o) can be determined from a previouslyidentified 1-1 match.

Depending on the processing resources available, instead of using thelinear interpolation presented above, we propose to use a look-up tablecontaining depth positions z for various (t_(e)−t_(h)) values for 1-1matches. This approach allows for a more accurate interpolation, sinceno linear interpolation approximation is assumed. For subsequent 1-2 and2-1 matches a 2D lookup table is created containing depth positions zfor each interaction in the 2-1 match for various z depth valuesidentified in a previous 1-1 match, and (t_(h,i)−t_(h)). A similarlook-up table will be created for 2-1 matches, by making a table of zdepth values for each interaction for various z depth values identifiedin a previous 1-1 match, and (t_(e,i)−t_(e)).

A more accurate analytic interpolation method for 1-1 matches is a cubicinterpolation. Such an interpolation fits much better the dependency ofthe depth z versus dT50 than a linear interpolation (see FIG. 6).

Besides the fact that charge carriers drift velocities are not constantacross the detector width, another factor contributing to a non-linearinterpolation function is the use of the T50 timing to represent thecharge carrier collection time. This is an approximation which becomescoarse for interactions taking place close to the detector electrodes,because of the superposition of strong signals induced by both theelectron and hole components.

Side scanning measurements have been performed to calibrate thez-interpolation (see FIG. 7). A cubic interpolation provided a very goodfit for the experimental points (see FIG. 6).

X-Y Interpolation

The positions of the interactions in the x-and y-directions can bedetermined with a precision better than the one provided by thesegmentation alone. As with the z-interpolation, this is done byanalyzing the signal waveforms. The physical property, which allows forinterpolating positions within the segment's borders is the fact thatthe amplitude of the transient signals induced in segments adjacent tothe Collecting segment falls approximately exponentially with thedistance to their borders. Therefore, by observing the difference in theamplitude norm of the transient signals in the two adjacent segments,information can be obtained about the position of the interactionrelative to the segment's border.

X-Y interpolation requires a new filter which extracts the amplitudenorm of the transient signals in adjacent segments synchronous in timewith the 50% crossing of the pulse in the collecting segments (T50). Amoving average filter with a time constant of 50 ns was used to cut-offsome of the high-frequency noise. The calculation of the amplitude asthe transient amplitude norm, (TAN) is done as following:

$\begin{matrix}{{{TAN} = {\sqrt{\sum\limits_{i = {n\; 1}}^{n\; 2}\; S_{i}^{2}} - {\sigma\sqrt{{n\; 2} - {n\; 1}}}}},} & (9)\end{matrix}$where S_(i) is the waveform sample amplitude, n1 and n2 represent theindices indicating the waveform window over which the amplitude norm iscalculated. The indices are represented in respect to the T50 timingsample index.

Further, to insure positive values after correcting for variance,TAN=max(TAN,1).  (10)

Once having measured the two amplitudes TAN_(left) and TAN_(right) ofthe two segments adjacent to the firing one, left and right, theirratio, R is:

$\begin{matrix}{R = {\frac{{TAN}_{right}}{{TAN}_{left}}.}} & (11)\end{matrix}$

The interpolated position in the direction perpendicular to thedirection of the strips is calculated as:

$\begin{matrix}{{r = {{PitchSize}\left( {\frac{2\;{{arctg}\left( R^{\beta} \right)}}{\pi} - \frac{1}{2}} \right)}},} & (12)\end{matrix}$where the exponent β is used to change the slope of the interpolationcurve, and has to be optimized for each individual detector.

According to the recent experimental results, this interpolationprovides a much more accurate representation of the interpolatedposition than a previous approach which only assumed a linearinterpolation formula.

Identification of Charge-Shared Interactions

Charge sharing is the process by which the charge carriers produced by asingle interaction are collected by two adjacent electrodes. It isimportant to identify such interactions in order to discriminate themfrom cases when multiple interactions induce signals in adjacentsegments. For example, in FIG. 12, we see two different 2-1 events-oneproduced by a single interaction with charge sharing and one by twointeractions. It is important to correctly identify which processproduced these signals to correctly image the gamma-ray.

The predominance of the charge sharing interactions is determined by theextension of their charge carrier clouds. The initial dimensions ofthese clouds are determined by the path of the Compton-electrons orphotoelectrons in the detection material. During the drift towardelectrodes, the clouds are further enlarged by the thermal diffusion,electrostatic repulsion between charge carriers, and other inelasticscattering mechanisms inside the crystal lattice.

The diffusion coefficient for electrons and holes D_(e,h) is:

$\begin{matrix}{D_{e,h} = {\frac{k_{B}T}{e}\mu_{e,h}}} & (13)\end{matrix}$where k_(B) is Boltzman's constant, μ_(e,h) is the electron and holemobility, T is the temperature of the crystal, e is the electron'scharge. The evolution of the charge carrier cloud during their drifttowards the electrodes as determined by the diffusion is represented inFIG. 13.

If the probability for an interaction to share charges between twoelectrodes is p, the expected fraction of events of N interactions thatcontain a number n of charge-shared interactions is found by thebinomial distribution:P(n,T)=C _(n) ^(T) p ^(n)(1−p)^(T-n),  (14)where p is the probability for the occurrence of a charge sharing case,C_(n) ^(T) is the combination of T elements taken n times, and T is thenumber of trials. In the present case, the number of trials, T=2N, whereN is the number of interactions (each interaction in a DSSD will createtwo chances for charge sharing, one for the AC segments, one for DCsegments). The probability for at least a charge sharing case in an Ninteraction event is the sum of all probabilities that 1, 2, . . . , 2Ncharge sharing cases will occur:P(n≧1,2N)=P(1,2N)+P(2,2N)+ . . . =1−P(0,2N)  (15)That is:P=1−(1−p)^(2N).Example 1: p=15%, N=3; P=62%. Example 2: p=20%, N=4; P=83%.

This high probability for at least a charge sharing instance in anygiven event suggests that charge sharing is a very important factor inthe event selection process, and needs to be accounted for.

The signals induced by a charge sharing interaction in the two adjacentsegments have the same shape within a certain time interval. This is asignificant feature that is used to discriminate such interactions. Thesimilarity of shapes can be explained by the fact that at the borderbetween two segments, the charge cloud path goes through similarweighting fields associated with the two segments. An example of inducedsignals is shown in FIG. 10.

Gap Test Version 1

Candidates for charge sharing interactions are the (2-1) triggerpatterns, with the two adjacent firing segments on one side. For suchcases, it is hypothesized that the case is a charge sharing interaction.A Chi square hypothesis test is used to check this hypothesis.

$\begin{matrix}{{\chi^{2} = {\frac{\sum\limits_{i = {sl}}^{sr}\;\left( {s_{1\; i} - m_{i}} \right)^{2}}{\sigma_{s_{1\; i}}^{2}} + \frac{\sum\limits_{i = {sl}}^{sr}\;\left( {s_{2\; i} - m_{i}} \right)^{2}}{\sigma_{s_{2\; i}}^{2}}}},} & (16)\end{matrix}$where s_(1i) is the sample amplitude of the first waveform, s_(2i) isthe sample amplitude of the second waveform, σ_(s) _(1i) and σ_(s) _(2i)are the sample standard deviations for the first waveform, and thesecond waveform, respectively. The sums run over a waveform segmentstarting with sample index sl and ending with the sample index sr asdetermined in respect to the sample closest to the point where theleading edge passes a low level threshold. m_(i) is a model for thesample of index i. For a charge shared event, we expect to haveidentical signal waveforms within the specified time interval. The modelm_(i) we choose is the average of the two waveforms:

$\begin{matrix}{m_{i} = {\frac{s_{1\; i} + s_{2\; i}}{2}.}} & (17)\end{matrix}$

If the sample standard deviation is the same for all samples of the twowaveforms, thenσ_(s) _(1i) =σs _(2i) =σ.  (18)The estimation of the sample standard deviation is done using a regionof the signal that does not contain pulses, but only noise:

$\begin{matrix}{\sigma = {\sqrt{\frac{1}{N}{\sum\limits_{i = 1}^{N}\;\left( {s_{i} - \overset{\_}{s}} \right)^{2}}}.}} & (19)\end{matrix}$As a result, the gap test based on the Chi square test becomes:

$\begin{matrix}{{gapTest} = {\frac{\sum\limits_{i = {sl}}^{sr}\;\left( {s_{1\; i} - s_{2\; i}} \right)^{2}}{\sigma^{2}}.}} & (20)\end{matrix}$

If the hypothesis is correct (i.e., the signals are from a singlesharge-shared interaction), the variation in the s_(ji) samples isexpected to follow a normal distribution. Thus, the gapTest distributionwill be a chi-square distribution. For a certain significance level, αto accept the hypothesis, an upper threshold for gapTest will be chosenfrom the critical value of the Chi square distribution:gapTest<x _(a)(χ_(N) ²),  (21)here N is the number of degrees of freedom.

As described below, this first version of a gap test has been testedwith experimental data and found to identify only a part ofcharge-shared events.

Gap Test Version 2

As described above, waveforms have similar shape when the chargecarriers drift relatively far from the collecting electrode. As aresult, the first version of our gap test algorithm produced goodresults for interactions taking place far from the collectingelectrodes, but could not identify the charge shared interactions takingplace close to the electrodes (see FIG. 15).

When the interaction takes place near the collecting segments, thesignal waveforms from the two strips are very different from each otherin the signal window used by the first version of the algorithm. In sucha case, the waveforms will have a similar shape only toward the tail ofthe pulse leading edge, and then, there will be an off-set in amplitudedetermined by the difference in the pulse amplitudes of the twosegments.

In order to identify near-electrode charge sharing interactions, theposition of the window will be moved, and a correction has to be madefor the difference in the amplitude between the two waveforms.Therefore, a two-step test is needed to identify both types of chargesharing interactions.

Another change in the gaptest formula as compared with the firstalgorithm is the introduction of a kE_(max) term. This term will relaxthe assumed standard deviation σ so that, in the case when the waveformssignal to noise ratio is large (as it will be at high energies), therelatively small differences between the two waveforms due to theslightly different weighting fields associated with the two segmentswill not be reflected in the chi-squared test.

With this modification, the first step in the gap test (to identifycharge sharing interactions far away from the collecting electrode is:

$\begin{matrix}{{{gapTest}\; 1} = \frac{\sum\limits_{i = L}^{L + W}\;\left( {S_{1\; i} - S_{2\; i}} \right)^{2}}{\sigma^{2} + \left( {kE}_{\max} \right)^{2}}} & (22)\end{matrix}$and is applied to the time window shown in FIG. 15, which starts whenthe pulse amplitudes exceed a low-level threshold L (typically set at 3times σ to avoid triggering this test on noise).

The second step in the gap test (to identify near-electrode chargesharing interactions) must include a correction for the pulse amplitudesE1 and E2, and thus is:

$\begin{matrix}{{{gapTest}\; 2} = \frac{\sum\limits_{i = {H - W}}^{H}\;\left( {S_{1\; i} - S_{2\; i} + E_{2} - E_{1}} \right)^{2}}{\sigma^{2} + \left( {kE}_{\max} \right)^{2}}} & (23)\end{matrix}$where the time window ends when one of the pulses exceeds an upper-levelthreshold H, typically 3 to 4 times σ below the total pulse amplitude.

By selecting the minimum of these two values:gapTest=min(gapTest1,gapTest2)  (24)we can apply the same hypothesis test as was discussed for the version 1of the gap test (equation (23)).Gap Test Experimental Results

The experimental setup pictured in FIG. 13 was used to check the gaptest algorithms. The results are graphically shown in FIGS. 14 and 15.The 1 mm diameter collimated beam was centered in the gap between twosegments. For firing adjacent segments, a chi-squared distribution isformed by the gapTest values.

The first version of the gap test algorithm shows that many of the 1-2and 2-1 events can be found outside the chi square distribution. Theseare the events that are not recognized by the test to have similarwaveforms, which would indicate the presence of multiple interactions.However, there is a very big difference in these numbers when moving theirradiation spot from the middle of the segment to the gap between twosegments. Monte Carlo simulations would suggest only a 7% increase inthe multiplicity of 1-2 events when changing the irradiation spot fromthe middle of the segment into the gap, whereas the experimental resultsshow a factor of 2 increase. Clearly, this test is not complete, failingto recognize some of the charge sharing interactions.

The gap test version 2, by comparison with the first version, providesmuch more consistent results. The difference between the numbers of 1-2events outside the chi square distribution varies by a factor of 20%,between the two irradiation points, much closer to the 7% expected fromMonte Carlo simulations. Higher amplitudes have been obtained for thechi square distribution when the irradiation of the detector takes placein the gap between segments, than in the middle of the segment. This isin agreement with a higher charge sharing probability when theinteractions take place in close proximity to the gap between segments.

A larger number of adjacent 1-2 (1x-2y) events than 2-1 (2x-1y) eventshas been noticed. This might be explained by different effectivediffusion coefficients for the electrons and holes.

A digital computer system can be programmed to perform the method ofthis invention. Once programmed to perform particular functions pursuantto instructions from program software that implements the method of thisinvention, such digital computer system in effect becomes aspecial-purpose computer particular to the method of this invention. Thetechniques necessary for this are well-known to those skilled in the artof computer systems.

Computer programs implementing the method of this invention willcommonly be distributed to users on a distribution medium such as floppydisk or CD-ROM. From there, they will often be copied to a hard disk ora similar intermediate storage medium. When the programs are to be run,they will be loaded either from their distribution medium or theirintermediate storage medium into the execution memory of the computer,configuring the computer to act in accordance with the method of thisinvention. All these operations are well-known to those skilled in theart of computer systems.

The term “computer-readable medium” encompasses distribution media,intermediate storage media, execution memory of a computer, and anyother medium or device capable of storing for later reading by acomputer a computer program implementing the method of this invention.

References

[Amma-00] M. Amman, P. N. Luke, “Three-dimensional position sensing andfield shaping in orthogonal-strip germanium gamma-ray detectors”, Nucl.Instr. Meth. A, 452 (1-2), pp. 155-166, 2000.

[Amro-03] S. Amrose, S. E. Boggs, W. Coburn, R. P. Lin and D. M. Smith“Calibration of 3D positioning in a Ge cross-strip detector”, NIM-A,Volume 505, Issues 1-2, 1 Jun. 2003, Pages 170-173.

[Hull-01] Hull, E. L. et al., SPIE Proceedings, Bellingham Wash., 4507,2001.

[Luke-92] Luke, P. N., Cork C. P, Madden, N. W., et al., “Amorphous-GeBipolar Clocking Contacts on Ge Detectors”, IEEE Trans. Nucl. Sci., 39,590, 1992.

[Miha-05] L. Mihailescu, K. M. Vetter, M. T. Burks, E. L. Hull, W. W.Craig, “SPEIR: a Ge Compton camera” NIM-A, accepted for publication2005.

[Wulf-03a] E. A. Wulf, J. Ampe, W. N. Johnson, R. A. Kroeger, J. D.Kurfess and B. F. Phlips “Timing methods for depth determination ingermanium strip detectors”, NIM-A, Volume 505, Issues 1-2, 1 Jun. 2003,Pages 178-182.

All documents cited or referenced herein (“herein cited documents”), andall documents cited or referenced in herein cited documents, togetherwith any manufacturer's instructions, descriptions, productspecifications, and product sheets for any products mentioned herein orin any document incorporated by reference herein, are herebyincorporated herein by reference.

The foregoing description of the invention has been presented forpurposes of illustration and description and is not intended to beexhaustive or to limit the invention to the precise form disclosed. Manymodifications and variations are possible in light of the aboveteaching. The embodiments disclosed were meant only to explain theprinciples of the invention and its practical application to therebyenable others skilled in the art to best use the invention in variousembodiments and with various modifications suited to the particular usecontemplated. The scope of the invention is to be defined by thefollowing claims.

1. A system, comprising: means for collecting data from an electrodesegment or electrode segments of a double-sided segmented detector(DSSD); means for calculating, using said data, a 3 dimensional positionfor each of a plurality of gamma-ray photon interactions in said DSSD,wherein said means for calculating a 3 dimensional position isconfigured for energy matching of a “2-1” segment-to-segmentconfiguration, wherein said means for calculating a 3 dimensionalposition is configured for performing a GapTest for a first segment anda second segment that are adjacent; and means for producing a list ofeach said 3 dimensional position for each interaction of said pluralityof gamma-ray photon interactions.
 2. The system of claim 1, wherein saidmeans for collecting data is configured for determining which segment ofsaid DSSD has collected a charge carrier.
 3. The system of claim 1,wherein said means for collecting data is configured for determining theamount of energy collected in a segment of said DSSD.
 4. The system ofclaim 1, wherein said means for collecting data is configured fordetermining the time at which a charge carrier arrives at a segment ofsaid DSSD.
 5. The system of claim 1, wherein said means for collectingdata is configured for determining the amplitude of the energy collectedin a segment adjacent to a segment of said DSSD that has collected acharge carrier.
 6. The system of claim 1, wherein said means forcollecting data is configured for collecting energy waveform data fromadjacent segments of said DSSD.
 7. The system of claim 1, wherein saidmeans for collecting data is configured for performing at least one stepselected from the group consisting of (i) determining which segment ofsaid. DSSD has collected a charge carrier, (ii) determining an amount ofenergy collected in a segment of said DSSD, (iii) determining a time atwhich a charge carrier arrives at a segment of said DSSD, (iv)determining an amplitude of energy collected in a segment adjacent to asegment of said DSSD that has collected a charge carrier and (v)collecting energy waveform data from adjacent segments of said DSSD. 8.The system of claim 1, wherein said means for collecting data isconfigured for (i) determining which segment of said DSSD has collecteda charge carrier, (ii) determining an amount of energy collected in asegment of said DSSD, (iii) determining a time at which a charge carrierarrives at a segment of said DSSD, (iv) determining an amplitude ofenergy collected in a segment adjacent to a segment of said DSSD thathas collected a charge carrier and (v) collecting energy waveform datafrom adjacent segments of said DSSD.
 9. The system of claim 1, whereinsaid means for calculating a 3 dimensional position is configured forenergy matching of a “1-1” segment-to-segment configuration.
 10. Thesystem of claim 1, wherein said means for calculating a 3 dimensionalposition is configured for interpolating z- and x-y-interaction positioncoordinates.
 11. The system of claim 10, wherein said means forcalculating a 3 dimensional position is configured for using said z- andx-y-interaction position coordinates to determine the position of asingle interaction.
 12. The system of claim 1, wherein said means forcalculating a 3 dimensional position is configured for checking eventintegrity to verify that the sum of the energies of all identifiedinteractions is consistent with the total energy deposited in said DSSD.13. The system of claim 1, wherein when a plurality of photons produce aplurality of interactions, said means for calculating a 3 dimensionalposition is configured for calculating and making a list of saidposition for each interaction of said plurality of interactions, theapparatus further configured for creating a representation of agamma-ray image from said list.
 14. An system, comprising: means forcollecting gamma-ray photon interaction produced data from an electrodesegment or electrode segments of a double-sided segmented detector(DSSD); and means for calculating, using said data, a 3 dimensionalposition of said gamma-ray photon interaction in said DSSD, wherein saidmeans for calculating a 3 dimensional position is configured for energymatching of a “3-1” segment-to-segment configuration, wherein said meansfor calculating a 3 dimensional position is configured for performing aGapTest on said “3-1” segment-to-segment configuration.
 15. The systemof claim 14, wherein said means for calculating a 3 dimensional positionis configured for a second step of interpolating z- and x-y-interactionposition coordinates.
 16. The system of claim 15, wherein said means forcalculating a 3 dimensional position is configured for using the resultsof said second step of interpolating z- and x-y-interaction positioncoordinates to determine the position of a single interaction.